Rectangular to Polar Conversion Calculator

Convert Cartesian (rectangular) coordinates to polar coordinates (radius and angle). This calculator helps you find the distance from the origin and the angle in radians or degrees from the positive x-axis.

Input Parameters

Calculation Results

Calculation Formula

The polar coordinates (r, θ) are calculated as:

Radius (r) = √(x² + y²)
Angle (θ) = arctan(y/x)
Where:
x = horizontal distance from origin
y = vertical distance from origin
r = distance from the origin
θ = angle measured from the positive x-axis

Radius (r):

Angle (θ):

Rectangular to Polar Conversion Calculator Usage Guide

Learn how to use the calculator to convert Cartesian coordinates to polar coordinates.

How to Use This Calculator

  1. Enter the X and Y coordinates in the input fields. These represent the horizontal and vertical distances from the origin.
  2. Select your preferred output format for the angle: Radians or Degrees.
  3. Click the "Calculate" button to convert the rectangular coordinates to polar coordinates.
  4. The results will show the radius (distance from origin) and the angle (θ) from the positive x-axis.

Understanding the Conversion

Cartesian coordinates (x, y) represent points on a plane based on their distance from the origin along the x and y axes. Polar coordinates (r, θ) represent the same points based on their distance from the origin (radius) and the angle from the positive x-axis.

The conversion formulas are:

  • Radius (r) = √(x² + y²) - This calculates the distance from the origin to the point.
  • Angle (θ) = arctan(y/x) - This calculates the angle from the positive x-axis, with consideration for the correct quadrant.

Example

If you have Cartesian coordinates (3, 4):

  • Radius = √(3² + 4²) = √(9 + 16) = √25 = 5
  • Angle = arctan(4/3) ≈ 53.13° (or approximately 0.927 radians)

So the polar coordinates would be (5, 53.13°) or (5, 0.927 rad).